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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Depth zero Boolean algebras


Author: Asher M. Kach
Journal: Trans. Amer. Math. Soc. 362 (2010), 4243-4265
MSC (2000): Primary 03D45
DOI: https://doi.org/10.1090/S0002-9947-10-05002-6
Published electronically: March 23, 2010
MathSciNet review: 2608405
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Abstract: We study the class of depth zero Boolean algebras, both from a classical viewpoint and an effective viewpoint. In particular, we provide an algebraic characterization, constructing an explicit measure for each depth zero Boolean algebra and demonstrating there are no others, and an effective characterization, providing a necessary and sufficient condition for a depth zero Boolean algebra of rank at most $ \omega$ to have a computable presentation.


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Additional Information

Asher M. Kach
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email: kach@math.uconn.edu

DOI: https://doi.org/10.1090/S0002-9947-10-05002-6
Keywords: Boolean algebras, Ketonen invariants, depth zero
Received by editor(s): June 9, 2008
Published electronically: March 23, 2010
Additional Notes: The author thanks his thesis advisor, Steffen Lempp, for all his guidance and suggestions; Christopher Alfeld, Robert Owen, and Daniel Turetsky for numerous conversations, comments, and corrections; and the anonymous referee for his/her comments.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.